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## Homework Statement

map the function [tex] \begin{equation}w = \Big(\frac{z-1}{z+1}\Big)^{2} \end{equation}[/tex]

on some domain which contains [tex]z=e^{i\theta}[/tex]. [tex]\theta[/tex] between 0 and [tex]\pi[/tex]

Hint: Map the semicircular arc bounding the top of the disc by putting [tex]$z=e^{i\theta}$[/tex] in the above formula. The resulting expression reduces to a simple trig function.

## Homework Equations

I can get the map if I can figure out what function they're going for, but I have no idea what function this is.

## The Attempt at a Solution

[tex]$$w = \Big(\frac{e^{i\theta}-1}{e^{i\theta}+1}\Big)^{2}$$[/tex]

Where the heck do I go from here?